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polarizability.f90
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polarizability.f90
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module polarizability
!
use accuracy, only : hik, ik, rk, rk, cl, out, vellgt, planck, &
avogno, boltz, pi, small_
use diatom_module, only : job, Intensity, quantaT, eigen, basis, Ndipoles, Nss, &
dipoletm, duo_j0, fieldT, poten, three_j, &
jmin_global,spinspin
use timer, only : IOstart, Arraystart, Arraystop, ArrayMinus, &
Timerstart, Timerstop, MemoryReport, &
TimerReport, memory_limit, memory_now
use symmetry, only : sym,correlate_to_Cs
private
public pol_tranint
real(rk), allocatable, save :: polarisability_me(:, :)
type DmatT
real(rk), pointer :: mat(:, :, :)
end type DmatT
type DimatT
integer(ik),pointer :: imat(:,:,:)
end type DimatT
type DkmatT
integer(ik),pointer :: kmat(:,:)
end type DkmatT
type ElevelT
integer(ik) :: jind ! J index
integer(ik) :: igamma
integer(ik) :: ilevel
end type ElevelT
type dipoleT
real(rk),pointer :: rot(:,:,:,:,:)
end type dipoleT
integer(ik) :: Neigenlevels
type(ElevelT), allocatable :: Elevel(:)
type(dipoleT), allocatable :: wigner(:,:) ! rot. component of matrix elems
contains
subroutine pol_tranint
! Obtain the partition function, polarisability transition moments,
! linestrengths, and intensities.
! Transition moments and intensities are computed by the call to
! pol_intensity subroutine.
integer(ik) :: info
integer(ik) :: nJ, jind
real(rk), allocatable :: Jval(:), q_part(:,:)
real(rk) :: Jmin, Jmax, Jval_min, Jval_, energy, &
beta, exp_en, part
integer(ik) :: ilevel, igamma, irrep, istate, parity_gu, isym
integer(ik) :: iverbose = 4
! initialise array of J values
! J = 0 always present, regardless of whether it is used in calculations
!
Jmin = minval(intensity%J(1:2))
Jmax = maxval(intensity%J(1:2))
!
Jmin = max(jmin_global, Jmin)
!
! we now count J states, starting from the lowest J = 0 or 0.5, to make
! sure all J > 0 are included in the line list for any intensity%J to
! guarantee consistent energy list numbering
!
! find lowest possible J value
Jval_min = 0
if (mod(nint(2.0_rk*job%j_list(1)),2) /= 0) Jval_min = 0.5_rk
Jval_min = max(jmin_global, Jval_min)
!
Jval_ = Jval_min
nJ = 1
!
! count the number of J states
do while (Jval_ < Jmax)
Jval_ = Jval_ + 1.0_rk
nJ = nJ + 1
enddo
!
allocate(Jval(nJ), stat = info)
if (info /= 0) stop 'pol_tranint allocation error: Jval - out of memory'
!
allocate(q_part(20, nJ), stat = info)
if (info /= 0) stop 'pol_tranint allocation error: q_part - out of memory'
!
Jval_ = Jval_min
jind = 1
Jval(jind) = Jval_
do while (Jval_ < Jmax)
jind = jind + 1
Jval_ = Jval_ + 1.0_rk
Jval(jind) = Jval_
enddo
!
call duo_j0(iverbose, Jval)
!
! include ZPE if not provided as part of intensity input
!
if (job%shift_to_zpe) then
!
do jind = 1, nJ
!
Jval_ = Jval(jind)
!
do igamma = 1, sym%NrepresCs
!
do ilevel = 1, eigen(jind, igamma)%Nlevels
!
energy = eigen(jind, igamma)%val(ilevel)
!
intensity%zpe = min(intensity%zpe, energy)
!
enddo
!
enddo
enddo
!
if (iverbose >= 4) &
write (out,"(/'Partition function = ',f18.4,' T = ',f12.2)") intensity%part_func,intensity%temperature
!
endif
!
select case (trim(intensity%action))
!
case('ABSORPTION', 'EMISSION', 'TM')
!
call Sort_levels(iverbose, nJ, Jval(1:nJ))
!
! run intensity simulations
!
beta = planck * vellgt / (boltz * intensity%temperature)
!
! compute partition function if not given
if (intensity%part_func < small_) then
!
intensity%part_func = 0
!
do jind = 1, nJ
!
Jval_ = Jval(jind)
!
do igamma = 1, sym%NrepresCs
!
do ilevel = 1, eigen(jind, igamma)%Nlevels
!
energy = eigen(jind, igamma)%val(ilevel)
irrep = eigen(jind, igamma)%quanta(ilevel)%igamma
!
! for homonuclear symmetries Nrepres = 4 and the irrep can be reconstucted baed on the parity and g/u:
istate = eigen(jind,igamma)%quanta(ilevel)%istate
parity_gu = poten(istate)%parity%gu
isym = correlate_to_Cs(igamma,parity_gu)
!
exp_en = exp(-(energy - intensity%ZPE) * beta)
!
intensity%part_func = intensity%part_func + intensity%gns(isym)*(2.0_rk*Jval_+1.0_rk) * exp_en
!
enddo
!
enddo
!
enddo
!
if (iverbose >= 4) write(out, "(/'Partition function = ', f18.4,'T = ', f12.2)") &
intensity%part_func, intensity%temperature
endif
!
call pol_intensity(Jval, iverbose)
!
write(out, '(/a)') 'done'
!
! compute parition function
case('PARTFUNC')
!
write(out, '(/a)') 'compute parition function'
!
beta = planck * vellgt / (boltz * intensity%temperature)
!
q_part = 0
!
! loop over J values
do jind = 1, nJ
!
Jval_ = Jval(jind)
!
do igamma = 1, sym%NrepresCs
!
do ilevel = 1, eigen(jind, igamma)%Nlevels
!
energy = eigen(jind, igamma)%val(ilevel)
irrep = eigen(jind, igamma)%quanta(ilevel)%igamma
!
! for homonuclear, symmetries Nrepres = 4, and the irrep can be
! reconstructed based on the parity and g/u:
istate = eigen(jind, igamma)%quanta(ilevel)%istate
parity_gu = poten(istate)%parity%gu
isym = correlate_to_Cs(igamma, parity_gu)
!
exp_en = exp(-(energy - intensity%ZPE) * beta)
!
q_part(irrep, jind) = q_part(irrep, jind)&
+ intensity%gns(isym)*(2.0_rk*Jval_+1.0_rk) * exp_en
!
enddo
!
enddo
enddo
!
part = sum(q_part(:,:))
!
do jind = 1, nJ
do irrep = 1, sym%NrepresCs
write(out, '(i4,1x,f18.1,1x,es16.8)') &
irrep, Jval(jind), q_part(irrep, jind)
enddo
enddo
!
write(out, '(es16.8)') part
!
end select
!
call MemoryReport
!
call TimerReport
!
end subroutine pol_tranint
!
!
!
function cg(j0, k0, dj, dk)
!
! Returns values for some Clebsch-Gordan coefficients
!
! Inputs:
! j0, k0 are j" and k" (initial state)
! dj, dk such that j0 + dj and k0 + dk are j' and k' (final state)
! Returns:
! cg = <j0 k0, 1 dk| j0 + dj j0 + dk>
!
integer(ik), intent(in) :: j0, k0, dj, dk
real(rk) :: cg
real(rk) :: j, m
j = real(j0, kind = rk)
m = real(k0 + dk, kind = rk)
cg = 0.0_rk
if (dj == 0 .and. dk == 0) cg = m / sqrt(j * (j + 1.0_rk))
if (dj == 0 .and. dk == 1) cg = -sqrt((j + m) * (j - m + 1.0_rk) / (2.0_rk * j * (j + 1.0_rk)))
if (dj == 0 .and. dk == -1) cg = sqrt((j - m) * (j + m + 1.0_rk) / (2.0_rk * j * (j + 1.0_rk)))
if (dj == 1 .and. dk == 0) cg = sqrt((j - m + 1.0_rk) * (j + m + 1.0_rk) / ((2.0_rk * j + 1.0_rk) * (j + 1.0_rk)))
if (dj == 1 .and. dk == 1) cg = sqrt((j + m) * (j + m + 1.0_rk) / ((2.0_rk * j + 1.0_rk) * (2.0_rk * j + 2.0_rk)))
if (dj == 1 .and. dk == -1) cg = sqrt((j - m) * (j - m + 1.0_rk) / ((2.0_rk * j + 1.0_rk) * (2.0_rk * j + 2.0_rk)))
if (dj == -1 .and. dk == 0) cg =-sqrt((j - m) * (j + m) / (j * (2.0_rk * j + 1.0_rk)))
if (dj == -1 .and. dk == 1) cg = sqrt((j - m) * (j - m + 1.0_rk) / (2.0_rk * j * (2.0_rk * j + 1.0_rk)))
if (dj == -1 .and. dk == -1) cg = sqrt((j + m + 1.0_rk) * (j + m) / (2.0_rk * j * (2.0_rk * j + 1.0_rk)))
return
end function cg
!
!
!
subroutine pol_intensity(Jval, iverbose)
! Calculates the polarisability transition moments and intensities
!
implicit none
!
real(rk),intent(in) :: Jval(:)
integer(ik),intent(in) :: iverbose
!
integer(ik) :: nJ, dimenmax
integer(ik) :: ilevelI, ilevelF
integer(ik) :: nlevelsG(sym%Nrepresen)
integer(ik) :: info, indI, indF, itransit, Ntransit, Nrepresen
integer(ik) :: igammaI, igammaF
integer(ik) :: dimenI, dimenF, nmax, parity_gu, isymI, isymF
real(rk) :: energyI, energyF, nu_if, linestr, linestr_zero, &
ener_, linestr2, linestr2_zero
real(rk) :: tm, jI, jF, ddot
logical :: passed, passed_
!
real(rk), allocatable :: vecI(:), vecF(:)
real(rk), allocatable :: half_linestr(:), half_linestr_zero(:)
!
integer(ik) :: jind, nlevels
!
integer(ik) :: iroot, NlevelsI, NlevelsF, nlower,iLF, iflag_rich
!
integer(ik) :: igamma_pair(sym%Nrepresen), igamma, istateI, istateF,&
ivibI, ivibF, ivI, ivF, ilambdaI, ilambdaF, iparityI, itau
real(rk) :: spinI, spinF, omegaI, omegaF, sigmaI, sigmaF
integer(hik) :: matsize
!
character(len=1) :: branch, ef, pm
character(len=2) :: dir
character(len=10) :: statename
!
type(quantaT),pointer :: quantaI, quantaF
!
real(rk) :: boltz_fc, beta, intens_cm_mol, emcoef,&
A_coef_s_1, A_einst, absorption_int
!
character(len=130) :: my_fmt !format for I/O specification
!
integer :: ndecimals
integer(ik) :: enunit, transunit
character(len=cl) :: filename, ioname
!
logical :: integer_spin = .true.
!
integer(ik) :: alloc_p
!
integer(ik) :: Jmax_, ID_J
real(rk) :: J_
!
character(len=12) :: char_Jf,char_Ji,char_LF
integer(ik), allocatable :: richunit(:,:)
character(len=2) :: let_LF ! richmol letters x,y,z
!
call TimerStart('Intensity calculations')
!
if (sym%maxdegen > 2) then
!
write(out, "('pol_intensity: this procedure has not been tested for symmetries with degeneracy higher than 2')")
!
endif
!
Nrepresen = sym%NrepresCs
!
! constants that will be needed
beta = planck * vellgt / (boltz * intensity%temperature)
intens_cm_mol = 8.0d-36 * pi**3 / (3.0_rk * planck * vellgt)
emcoef = planck*vellgt / (4.0_rk*pi)
A_coef_s_1 = 64.0d-36 * pi**4 / (3.0_rk * planck)
!
nJ = size(Jval)
!
! open units for the line list in the Exomol format
! the next section establishes the files to which the line intensities
! and energies will be written
if (trim(intensity%linelist_file)/="NONE") then
!
! open the '.states' file, which contains the energy levels themselves
filename = trim(intensity%linelist_file)//'.states'
write(ioname, '(a, i4)') 'Energy file' ! heading
call IOstart(trim(ioname), enunit)
open(unit = enunit, action = 'write', &
status = 'replace', file = filename)
!
! open the '.tans' file, which contains the positions and A coeffs.
! of the spectral lines
filename = trim(intensity%linelist_file)//'.trans'
write(ioname, '(a, i4)') 'Transition file' ! heading
call IOstart(trim(ioname), transunit)
open(unit = transunit, action = 'write', &
status = 'replace', file = filename)
!
if (intensity%matelem) then
!
Jmax_ = nint(maxval(Jval(:)))
!
allocate(richunit(nJ, nJ)) ! used to mrk I/O unit
!
! we now begin writing the matrix elements to the file
do indI = 1, nJ
!
jI = Jval(indI)
!
write(char_jI, '(i12)') nint(jI)
!
do indF = 1, nJ
!
jF = Jval(indF)
!
if (Jf<Ji) cycle
!
! selection rules for SECOND rank spherical component
if(nint(abs(jI - jF)) > 2) cycle
!
write(char_jF, '(i12)') nint(jF)
!
! New Richmol format - one file for all components
!
! open the file for the matrix elements of the i-th lab component
filename = &
"matelem_ALPHA"//"_j"//trim(adjustl(char_jI))//"_j"//trim(adjustl(char_jF))//"_"//trim(intensity%linelist_file)//".rchm"
!
call IOstart(trim(filename), richunit(indI, indF))
open(unit = richunit(indI, indF), action = 'write', &
status='replace', file=filename)
!
write(richunit(indI, indF), "('Start richmol format')")
!
! 2nd rank tensor, with 6 non-zero components
write(richunit(indI, indF), "('ALPHA',' 2',' 6')")
write(richunit(indI, indF), "('M-tensor')")
!
! Nine lab-frame polarisability tensor components
do iLF = 1,6
!
let_LF = "xx"
if (iLF == 2) let_LF = "xy"
if (iLF == 3) let_LF = "xz"
if (iLF == 4) let_LF = "yy"
if (iLF == 5) let_LF = "yz"
if (iLF == 6) let_LF = "zz"
if (iLF == 7) let_LF = "yx"
if (iLF == 8) let_LF = "zx"
if (iLF == 9) let_LF = "zy"
!
! flag is -1 when sum over alpha^k_m has prefactor of i
iflag_rich = 0
!if (iLF == 2 .or. iLF == 5) iflag_rich = -1
if (iLF == 2 .or. iLF == 5 .or. iLF == 7 .or. iLF == 9) iflag_rich = -1
!
write(char_LF, '(i12)') iLF
!
write(richunit(indI, indF), "('alpha',i5,i3,1x,a2)") &
iLF, iflag_rich, let_LF
!
! call subroutine to calculate LF portion of matrix elements
call do_LF_matrix_elements(iLF, richunit(indI, indF), jI, jF)
enddo
!
write(richunit(indI, indF), "('K-tensor')")
!
enddo
enddo
endif
!
endif
!
! maximal size of basis functions
!
dimenmax = 0
!
! loop over J values
!
do jind = 1, nJ
do igamma = 1, Nrepresen
!
! Estimate the maximal size of basis functions
dimenmax = max(dimenmax, eigen(jind, igamma)%Ndimen)
!
enddo
enddo
!
Nmax = nint(Jval(nJ)) + 1
!
! We now count the number of non-zero transitions, this will help keep
! keep track of the calculation process.
!
Ntransit = 0
!
! number of inital states
nlevels = Neigenlevels
!
! For a given symmetry (igamma) with some gns(igamma), we find it's
! counterpart jgamma /= igamma having the same gns(jgamma). We assume
! that there is only one such pair in the case of absorption or emission
!
call find_igamma_pair(igamma_pair)
!
call TimerStart('Intens_Filter-1')
!
ener_ = 0
nlower = 0
iroot = 0
!
! loop over initial states
do indI = 1, nJ
!
! rotational quantum number
jI = Jval(indI)
!
! loop for each symmetry
do igammaI = 1, Nrepresen
!
nlevelsI = eigen(indI, igammaI)%Nlevels
!
! loop over energy levels in initial J state
do ilevelI = 1, nlevelsI
!
! energy and quanta of initial state
energyI = eigen(indI, igammaI)%val(ilevelI)
istateI = eigen(indI, igammaI)%quanta(ilevelI)%istate
parity_gu = poten(istateI)%parity%gu
isymI = correlate_to_Cs(igammaI, parity_gu)
!
call energy_filter_lower(jI, energyI, passed)
!
if (.not. passed) cycle
!
nlower = nlower + 1
!
! loop over final states
do indF = 1, nJ
!
jF = jval(indF)
!
do igammaF = 1, Nrepresen
!
nlevelsF = eigen(indF, igammaF)%Nlevels
!
! loop over energy levels in final J state
do ilevelF = 1, nlevelsF
!
! energy and quanta of final state
energyF = eigen(indF, igammaF)%val(ilevelF)
istateF = eigen(indF, igammaF)%quanta(ilevelF)%istate
parity_gu = poten(istateF)%parity%gu
isymF = correlate_to_Cs(igammaF, parity_gu)
!
call intens_filter(jI, jF, energyI, energyF, isymI, &
isymF, igamma_pair, passed)
!
if (intensity%matelem) call matelem_filter(jI, jF, energyI,&
energyF, isymI, isymF, igamma_pair, passed)
!
! if transition is non-zero then increment counter
if (passed) then
!
Ntransit = Ntransit + 1
!
endif
enddo
enddo
enddo
enddo
enddo
enddo ! end of transition counting
!
call TimerStop('Intens_Filter-1')
!
! loop over final states -> count states for each symmetry
!
nlevelsG = 0
!
! guess if half-integer spin case
if (mod(eigen(1, 1)%quanta(1)%imulti, 2) == 0) integer_spin = .false.
!
allocate(vecI(dimenmax), stat = info)
call ArrayStart('intensity-vecI', info, size(vecI), kind(vecI))
!
do indI = 1, nJ
!
! rotational quantum number
jI = jval(indI)
J_ = -1 ! for Richmol count
!
do igammaI = 1, Nrepresen
!
nlevelsI = eigen(indI, igammaI)%Nlevels
dimenI = eigen(indI, igammaI)%Ndimen
!
do ilevelI = 1, nlevelsI
!
! energy and symmetry of the state
energyI = eigen(indI, igammaI)%val(ilevelI)
!
istateI = eigen(indI, igammaI)%quanta(ilevelI)%istate
parity_gu = poten(istateI)%parity%gu
! C2v/Cs symmetry
isymI = correlate_to_Cs(igammaI, parity_gu)
!
! ignore states with zero nuclear weight
if (intensity%gns(isymI) < small_) cycle
!
iroot = iroot + 1
eigen(indI, igammaI)%quanta(ilevelI)%iroot = iroot
!
if (trim(intensity%linelist_file) /= "NONE") then
!
! dimension of the basis for initial states
!
! energy, quanta, and degeneracy order of the initial state
quantaI => eigen(indI, igammaI)%quanta(ilevelI)
ivibI = quantaI%ivib
ivI = quantaI%v
sigmaI = quantaI%sigma
spinI = quantaI%spin
ilambdaI = quantaI%ilambda
omegaI = quantaI%omega
iparityI = quantaI%iparity
statename = trim(quantaI%name)
!
! reconstruct +/- and e/f parities
pm = "+" ; if (iparityI == 1) pm = "-"
ef = "e"
!
if (mod(nint(2.0 * jI), 2) == 1) then
itau = mod(nint(jI - 0.5), 2)
else
itau = mod(nint(jI), 2)
endif
!
if (itau /= iparityI) then
ef = "f"
endif
!
! the variable 'ndecimals' gives the number of decimal digits to
! print the values of the energy levels to.
! we use 6 decimals for energy levels up to 100,000 cm-1 before
! sacrificing decimals to fit larger values in 12 spaces.
! this format works for energy levels larger than -10,000 cm-1 and
! less than 1e11 cm-1 - Lorenzo Lodi
!
ndecimals = 6 - max(0, int(log10(abs(energyI - intensity%ZPE) + 1.d-6) - 4))
!
if ( intensity%matelem ) then
!
ndecimals=6-max(0, int( log10(abs(energyI-intensity%ZPE)+1.d-6)-4) )
!
if (nint(2*Ji)/=nint(2*J_)) then
!
J_ = Ji
ID_J = 0
!
endif
!
ID_J = ID_J + 1
quantaI%iJ_ID = ID_J
!
if (integer_spin) then
!
write(my_fmt,'(a)') "(i6,1x,i8,1x,i2,1x,i2,3x,e21.14,5x,a4,i3,1x,a2,i4,1x,a2,f8.4,1x,i6,1x,i6,1x,i4,1x,i6,1x,a1,1x,a10)"
write(enunit,my_fmt) &
nint(J_),ID_J,iparityI+1,1,energyI-intensity%ZPE,'tau:',iparityI,'j:',nint(J_),'c',1.000_rk,nint((omegaI)),&
ivI,(ilambdaI),nint((sigmaI)),pm,statename
!
else
!
!stop 'not tested'
!
write(my_fmt,'(A,i0,a)') "(i7,1x,i12,1x,i1,1x,i2,1x,f12.",ndecimals,",1x,f7.1,1x,i6,1x,i4,1x,f7.1,1x,a1,1x,a10)"
write(enunit,my_fmt) &
int(J_),ID_J,iparityI+1,1,energyI-intensity%ZPE,omegaI,&
ivI,(ilambdaI),sigmaI,pm,statename
!
endif
!
else
!
ndecimals=6-max(0, int( log10(abs(energyI-intensity%ZPE)+1.d-6)-4) )
if (integer_spin) then
!
write(my_fmt,'(A,i0,a)') "(i12,1x,f12.",ndecimals,",1x,i6,1x,i7,1x,a1,1x,a1,1x,a10,1x,i3,1x,i2,2i8)"
write(enunit,my_fmt) &
iroot,energyI-intensity%ZPE,nint(intensity%gns(isymI)*( 2.0_rk*jI + 1.0_rk )),nint(jI),&
pm,ef,statename,ivI,(ilambdaI),nint((sigmaI)),nint((omegaI))
!
else
!
write(my_fmt,'(A,i0,a)') "(i12,1x,f12.",ndecimals,",1x,i6,1x,f7.1,1x,a1,1x,a1,1x,a10,1x,i3,1x,i2,2f8.1)"
write(enunit,my_fmt) &
iroot,energyI-intensity%ZPE,nint(intensity%gns(isymI)*( 2.0_rk*jI + 1.0_rk )),jI,&
pm,ef,statename,ivI,(ilambdaI),(sigmaI),(omegaI)
!
endif
!
endif
!
endif
!
call energy_filter_upper(jI, energyI, passed)
!
call energy_filter_lower(jI, energyI, passed_)
!
if (.not. passed .and. .not. passed_) cycle
!
istateI = eigen(indI, igammaI)%quanta(ilevelI)%istate
parity_gu = poten(istateI)%parity%gu
isymI = correlate_to_Cs(igammaI, parity_gu)
!
nlevelsG(isymI) = nlevelsG(isymI) + 1
!
enddo
enddo
enddo
!
deallocate(vecI)
call ArrayStop('intensity-vecI')
!
if (trim(intensity%linelist_file) /= "NONE") close(enunit, status='keep')
!
write(my_fmt,'(A,I0,A)') &
"('Number of states for each symm = ',", sym%Nrepresen, "i8)"
!
write(out,my_fmt) nlevelsG(:)
!
matsize = int(sum(nlevelsG(:)), hik)
!
if (iverbose >= 4) write(out,"(/'Dipole moment integration (i)...')")
!
if (Ntransit == 0) then
write(out,"('pol_intensity: the transition filters are too tight: no entry')")
!
stop 'pol_intensity: the filters are too tight'
endif
!
write(out, "(/'...done!')")
!
allocate(vecI(dimenmax), vecF(dimenmax), stat=info)
!
call ArrayStart('intensity-vectors', info, size(vecI), kind(vecI))
call ArrayStart('intensity-vectors', info, size(vecF), kind(vecF))
!
! loop over final states -> count states for each symmetry
!
write(my_fmt,'(A,I0,A)') &
"('Number of states for each symm = ',", sym%Nrepresen, "i8)"
!
write(out,my_fmt) nlevelsG(:)
!
if (iverbose >= 0) then
write(out, "(' Total number of lower states = ',i8)") nlower
write(out, "(' Total number of transitions = ',i8)") Ntransit
end if
!
if (iverbose >= 0) then
write(out, "(/' Statistical weights gns = ',4f12.1)") intensity%gns(1:)
end if
!
! To speed up the line strength evaluation, we perform the calculation:
! S_{if} = | <i|a|f> |^2 = | \sum_{nm} C_in C_fm <n|a|m> |^2
! in three steps:
! 1. Evaluate the expansion of the initial state:
! s_{im} = sum_{n} C_in <n|a|m>
! 2. Evaluate the product with the expansion of the final state:
! s_{if} = sum_{m} C_fm s_{im}
! 3. Square the result to obtain S_{if}
! S_{if} = s_{if}^2
!
! The temporary object s_{im} is referred to as the 'half linestrength',
! with corresponding variable "half_linestr".
!
allocate(half_linestr(dimenmax), stat = info)
allocate(half_linestr_zero(dimenmax), stat = info)
!
call ArrayStart('half_linestr', info, size(half_linestr), &
kind(half_linestr))
!
if (iverbose >= 5) call MemoryReport
!
write(out,"(/a,a,a,a)") &
'Linestrength S(f<-i) [Debye**2],', ' Transition moments [Debye],', &
' Einstein coefficient A(if) [1/s],', ' and Intensities [cm/mol]'
!
! Prepare the table header
!
select case (trim(intensity%action))
!
case('ABSORPTION')
!
write(out, &
"(/t5,'J',t7,'Gamma <-',t18,'J',t21,'Gamma',t27,'Typ',t37,'Ei',&
&t44,'<-',t52,'Ef',t64,'nu_if',8x,'S(f<-i)',10x,'A(if)',12x,&
&'I(f<-i)',7x,'State v lambda sigma omega <- State v lambda&
& sigma omega ')")
!
dir = '<-'
!
case('EMISSION')
!
write(out, &
"(/t5,'J',t7,'Gamma ->',t18,'J',t21,'Gamma',t27,'Typ',t37,'Ei',&
&t44,'->',t52,'Ef',t64,'nu_if',8x,'S(i->f)',10x,'A(if)',12x,&
&'I(i->f)',7x,'State v lambda sigma omega -> State v lambda&
& sigma omega ')")
!
dir = '->'
!
case('TM')
!
write(out,"(/t4,'J',t6,'Gamma <-',t17,'J',t19,'Gamma',t25,'Typ',t35,'Ei',&
&t42,'<-',t52,'Ef',t65,'nu_if',10x,'TM(f->i)')")
!
!
end select
!
deallocate(vecF)
!
! ---------------------------------
! The actual intensity calculations
! ---------------------------------
!
itransit = 0
!
! loop over initial states
do indI = 1, nJ
!
jI = jval(indI)
!
! loop over initial state symmetries
do igammaI = 1, Nrepresen
!
! number of sublevels and dimension of basis for initial state
nlevelsI = eigen(indI, igammaI)%Nlevels
dimenI = eigen(indI, igammaI)%Ndimen
!
! loop over final states
do indF = 1, nJ
!
jF = jval(indF)
!
! selection rules for irreducible second & zeroth rank
! spherical polarisability tensor components
if (abs(nint(jI - jF)) > 2 ) cycle
!
! loop over final state symmetries
do igammaF = 1, Nrepresen
!
! number of sublevels and dimension of basis for final state
nlevelsF = eigen(indF, igammaF)%Nlevels
dimenF = eigen(indF, igammaF)%Ndimen
!
Ilevels_loop : do ilevelI = 1, nlevelsI
!
! energy, quanta and degeneracy of the initial state
energyI = eigen(indI, igammaI)%val(ilevelI)
!
quantaI => eigen(indI, igammaI)%quanta(ilevelI)
istateI = quantaI%istate
ivibI = quantaI%ivib
ivI = quantaI%v
sigmaI = quantaI%sigma
spinI = quantaI%spin
ilambdaI = quantaI%ilambda
omegaI = quantaI%omega
!
! reconstruct symmetry for C2v which is different to Cs case
parity_gu = poten(istateI)%parity%gu
isymI = correlate_to_Cs(igammaI, parity_gu)
!
call energy_filter_lower(jI, energyI, passed)
!
if (.not. passed) cycle
!
vecI(1:dimenI) = eigen(indI, igammaI)%vect(1:dimenI, ilevelI)
!
! Compute the half-linestrength
!
! if no transitions from ilevelI -> jF exist then skip
! calculation, so we check for this condition
passed = .false.
!
! loop over final states
do ilevelF = 1, nlevelsF
!
! energy and quanta of final state
energyF = eigen(indF,igammaF)%val(ilevelF)
!
quantaF => eigen(indF,igammaF)%quanta(ilevelF)
istateF = quantaF%istate
ivibF = quantaF%ivib
ivF = quantaF%v
sigmaF = quantaF%sigma
spinF = quantaF%spin
ilambdaF = quantaF%ilambda
omegaF = quantaF%omega
!
! reconstruct symmetry for C2v which is different to Cs case
parity_gu = poten(istateF)%parity%gu
isymF = correlate_to_Cs(igammaF, parity_gu)
!
call intens_filter(jI, jF, energyI, energyF, isymI, isymF, &
igamma_pair, passed)
!
! prevents diagonal matrix elements from being skipped
if (intensity%matelem) &
call matelem_filter(jI, jF, energyI, energyF, isymI, isymF,&
igamma_pair,passed)
!
! stop checking when a transition passed the filter
if (passed) exit
!
enddo
!
! if no transition pass the filter, cycle to next state
if (.not. passed) cycle
!
select case (trim(intensity%action))
!
case('ABSORPTION', 'EMISSION')
!
if (isymF /= igamma_pair(isymI)) cycle
!
if ((intensity%J(1) + intensity%J(2) > 0) &
.and. abs(nint(jI - jF)) <= 2 ) then
!
call do_1st_half_linestrength(jI, jF, indI, indF, dimenI, &
dimenF, vecI(1:dimenI), &
half_linestr, &
half_linestr_zero)
!
endif
!
case('TM')
!
call do_1st_half_tm(indI, indF, dimenI, dimenF, &
vecI(1:dimenI), half_linestr)
!
end select
!
! loop over final states
allocate(vecF(dimenmax), stat = alloc_p)
!
if (alloc_p /= 0) then
write(out, &
"(' dipole: ',i9,' trying to allocate array -vecF')") &
alloc_p
!
stop 'dipole-vecF - out of memory'
!
end if
!
Flevels_loop : do ilevelF = 1, nlevelsF
!
! energy and quanta of final state
energyF = eigen(indF, igammaF)%val(ilevelF)
!
! dimension of bases for final state
dimenF = eigen(indF, igammaF)%Ndimen
!
quantaF => eigen(indF, igammaF)%quanta(ilevelF)
!
istateF = quantaF%istate
ivibF = quantaF%ivib
ivF = quantaF%v
sigmaF = quantaF%sigma
spinF = quantaF%spin
ilambdaF = quantaF%ilambda
omegaF = quantaF%omega
!
call energy_filter_upper(jF, energyF, passed)
!
if (.not.passed) cycle Flevels_loop
!
parity_gu = poten(istateF)%parity%gu
isymF = correlate_to_Cs(igammaF, parity_gu)
!
call intens_filter(jI, jF, energyI, energyF, isymI, isymF,&
igamma_pair, passed)
!
if (intensity%matelem) &
call matelem_filter(jI, jF, energyI, energyF, isymI, &
isymF, igamma_pair, passed)
!
if (.not. passed) cycle Flevels_loop
!
! Find PQR branch for transition
branch = PQR_branch(jI, jF)
!
nu_if = energyF - energyI
!
! filer out zero-frequency transitions
if (nu_if < small_) cycle
!
! Count processed transitions
itransit = itransit + 1
!
vecF(1:dimenF) = eigen(indF, igammaF)%vect(1:dimenF, ilevelF)
!
select case (trim(intensity%action))
!
case default
!
stop 'only ABSORPTION and TM are properly coded'
!
case('ABSORPTION', 'EMISSION')
!
linestr = ddot(dimenF, half_linestr, 1, vecF, 1)
linestr_zero = ddot(dimenF, half_linestr_zero, 1, vecF, 1)
!
linestr2 = linestr**2
linestr2_zero = linestr_zero**2
!
!
! calculate intensity
A_einst = A_coef_s_1 * (2.0_rk * jI + 1.0_rk) &
* linestr2 * abs(nu_if)**3